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arXiv 1306.4610cond-mat.quant-gascond-mat.str-elmath-phmath.MPquant-ph
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一维强相互作用受限量子系统

Strongly interacting confined quantum systems in one dimension

A. G. Volosniev, D. V. Fedorov, A. S. Jensen, M. Valiente, N. T. Zinner

摘要:

在一个维度上,对磁性的研究可以追溯到量子力学的黎明,当时贝特解决了描述磁性系统量子行为的著名海森堡模型。在过去的十年中,一维系统已经成为研究的前沿领域,这是由使用冷原子气体实现Tonks-Girardeau气体驱动的。在这里,我们证明了具有强短程相互作用的一维费米子和玻色子系统是可解的,在任意限制的几何形状,通过引入一种新的能量泛函技术,并获得完整的能量谱和本征态。作为第一个应用程序,我们计算空间相关性,并显示如何铁磁和反铁磁状态已经存在的小系统尺寸,在当前的实验中准备和研究。我们的工作展示了在微观尺度上对磁关联进行量子操纵的巨大潜力。

英文摘要:

In one dimension, the study of magnetism dates back to the dawn of quantum mechanics when Bethe solved the famous Heisenberg model that describes quantum behaviour in magnetic systems. In the last decade, one-dimensional systems have become a forefront area of research driven by the realization of the Tonks-Girardeau gas using cold atomic gases. Here we prove that one-dimensional fermionic and bosonic systems with strong short-range interactions are solvable in arbitrary confining geometries by introducing a new energy-functional technique and obtaining the full spectrum of energies and eigenstates. As a first application, we calculate spatial correlations and show how both ferro- and anti-ferromagnetic states are present already for small system sizes that are prepared and studied in current experiments. Our work demonstrates the enormous potential for quantum manipulation of magnetic correlations at the microscopic scale.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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